This document describes observations of the Seyfert 1 galaxy Mrk 509 using the Cosmic Origins Spectrograph (COS) on the Hubble Space Telescope (HST). The observations detected absorption features in the ultraviolet spectrum, which are attributed to outflowing gas from the active galactic nucleus as well as gas in the galaxy's interstellar medium and halo. The COS observations provide higher signal-to-noise and resolution than previous observations, detecting additional complexity in the absorption features. Variability in some features constrains the distances of absorbing gas components to be less than 250 pc and 1.5 kpc from the active nucleus. The absorption lines only partially cover the emission from the active nucleus, possibly due to